{"id":4680,"date":"2023-05-05T10:00:58","date_gmt":"2023-05-05T04:30:58","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=4680"},"modified":"2023-05-06T09:19:32","modified_gmt":"2023-05-06T03:49:32","slug":"construction-of-angles-using-compass-ruler","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/construction-of-angles-using-compass-ruler\/","title":{"rendered":"How Do You Construct An Angle With Compass And Ruler"},"content":{"rendered":"

Construction Of An Angle Using\u00a0Compass And Ruler<\/strong><\/h2>\n

To draw an angle equal to a given angle<\/strong><\/h3>\n

In this section, we will learn how to construct angles of 60\u00ba, 30\u00ba, 90\u00ba, 45\u00ba and 120\u00ba with the help of ruler and compasses only.<\/p>\n

Construction Of Some Standard Angles<\/h3>\n

Construction of an Angle of 60\u00ba<\/strong>
\nIn order to construct an angle of 60\u00ba with the help of ruler and compasses only, we follow the following steps :
\n\"How
\nSteps of Construction<\/strong>
\nStep I:<\/strong> Draw a ray OA.
\nStep II:<\/strong> With centre O and any radius draw an arc PQ with the help of compasses, cutting the ray OA at P.
\nStep III:<\/strong> With centre P and the same radius draw an arc cutting the arc PQ at R.
\nStep IV:<\/strong> Join OR and produce it to obtain ray OB.
\nThe angle \u2220AOB so obtained is the angle of measure 60\u00ba.<\/p>\n

Justification:<\/strong> In above figure, join PR.
\nIn \u0394OPR, we have
\nOP = OR = PR
\n\u21d2 \u0394OPR is an equilateral triangle.
\n\u21d2 \u2220POR = 60\u00ba
\n\u21d2 \u2220AOB = 60\u00ba [\u2235 \u2220POR = \u2220AOB]<\/p>\n

(ii) Construction of An Angle of 30\u00ba<\/strong>
\n\"How
\nSteps of Construction:<\/strong>
\nStep I:<\/strong> Draw \u2220AOB = 60\u00ba by using the steps mentioned above.
\nStep II:<\/strong> With centre O and any convenient radius draw an arc cutting OA and OB at P and Q respectively.
\nStep III:<\/strong> With centre P and radius more than \\(\\frac { 1 }{ 2 } \\)(PQ), draw an arc in the interior of \u2220AOB.
\nStep IV:<\/strong> With centre Q and the same radius, as in step III, draw another arc intersecting the arc in step III at R.
\nStep V:<\/strong> Join OR and product it to any point C.
\nStep VI:<\/strong> The angle \u2220AOC is the angle of measure 30\u00ba.<\/p>\n

(iii) Construction of An Angle of 90\u00ba<\/strong>
\n\"How
\nSteps of Construction:<\/strong>
\nStep I:<\/strong> Draw a ray OA.
\nStep II:<\/strong> With O as centre and any convenient radius, draw an arc, cutting OA at P.
\nStep III:<\/strong> With P as centre and the same radius, an arc cutting the arc drawn in step II at Q.
\nStep IV:<\/strong> With Q as centre and the same radius as in steps II and III, draw an arc, cutting the arc drawn in step II at R.
\nStep V:<\/strong> With Q as centre and the same radius, draw an arc.
\nStep VI:<\/strong> With R as centre and the same radius, draw an arc, cutting the arc drawn in step V at B.
\nStep VII:<\/strong> Draw OB and produce it to C. \u2220AOC is the angle of measure 90\u00ba.<\/p>\n

(iv) Construction of An Angle of 45\u00ba<\/strong>
\n\"How
\nSteps of Construction:<\/strong>
\nStep I:<\/strong> Draw \u2220AOB = 90\u00ba by following the steps given above.
\nStep II:<\/strong> Draw OC, the bisector of \u2220AOB.
\nThe angle \u2220AOC so obtained is the required angle of measure 45\u00ba.<\/p>\n

(v) Construction of An Angle of 120\u00ba<\/strong>
\n\"How
\nSteps of Construction:<\/strong>
\nStep I:<\/strong> Draw a ray OA.
\nStep II:<\/strong> With O as centre and any convenient radius, draw an arc cutting OA at P.
\nStep III:<\/strong> With P as centre and the same radius draw an arc, cutting the first arc at Q.
\nStep IV:<\/strong> With Q as centre and the same radius, draw an arc, cutting the arc drawn in step II at R.
\nStep V:<\/strong> Join OR and produce it to any point C. \u2220AOC so obtained is the angle of measure 120\u00ba.<\/p>\n

Read More:<\/strong><\/p>\n